For the first question: TESTING! Something is eatable if it does not contain toxins(you can find that out from a chemical analysis). The expiration date is determined experimentaly: they simply see when things start growing on it 😉 😉
Really depends on the vitamin. But i am guessing that since most vitamins have excipients like fructose and glucose bacteria can grow and them and that is not safe…

The expiration date is usually dependent the packaging. Tinned foods last 3-5 years. Honey lasts forever. For things such as fresh milk, I guess they’ll have to experimentally determine it like MrMistery mentioned.

Oh yeah mithril is right. It depends on what you put in also. What i was saying was only if you sell it without rapping it 😉

Can be more complicated, mostly when dealing with produce are highly susceptible of bacterial contamination. Experimenting is sure usefull, but sometimes things like predictive microbiology (modelling bacterial growth in order to determine statisically a safe limit for consumption…).

For chemicals like vitamins often sold as a powder, though, bacteria are not a problem if properly stored. They do not grow when there is not enough water, and sugar do not help since in solution the reduce the disponibility of water (that is why jam can be stored) and prevents bacterial and fungal growth. The limit is more the stability of the vitamin over time. Past expiration date either you have a dose of vitamin that is so much below the one presented that the produce is not worth taking anymore or it degrades in chemicals taht should not be ingested, hence you should not ingest it. I do not know what is happening for particular molecules, but you better trust the label for pharmaceuticals.

Patrick

I think, they also use the half-life of substances to determine the expire-time. am I right?

half life is usually for atomic decay

Oh, sorry…I mean like this..the researcher also determine the expire date by measuring the half-life of the food substances. Am I right?